A12795. Paint the Numbers

You are given a sequence of integers $a_1, a_2, \dots, a_n$ . You need to paint elements in colors, so that:

- If we consider any color, all elements of this color must be divisible by the minimal element of this color.
- The number of used colors must be minimized.

For example, it's fine to paint elements $[40, 10, 60]$ in a single color, because they are all divisible by $10$ . You can use any color an arbitrary amount of times (in particular, it is allowed to use a color only once). The elements painted in one color do not need to be consecutive.

For example, if $a=[6, 2, 3, 4, 12]$ then two colors are required: let's paint $6$ , $3$ and $12$ in the first color ( $6$ , $3$ and $12$ are divisible by $3$ ) and paint $2$ and $4$ in the second color ( $2$ and $4$ are divisible by $2$ ). For example, if $a=[10, 7, 15]$ then $3$ colors are required (we can simply paint each element in an unique color).

The first line contains an integer $n$ ( $1 \le n \le 100$ ), where $n$ is the length of the given sequence.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 100$ ). These numbers can contain duplicates.

Print the minimal number of colors to paint all the given numbers in a valid way.

In the first example, one possible way to paint the elements in $3$ colors is:

- paint in the first color the elements: $a_1=10$ and $a_4=5$ ,
- paint in the second color the element $a_3=3$ ,
- paint in the third color the elements: $a_2=2$ , $a_5=4$ and $a_6=2$ .

In the second example, you can use one color to paint all the elements.

In the third example, one possible way to paint the elements in $4$ colors is:

- paint in the first color the elements: $a_4=4$ , $a_6=2$ and $a_7=2$ ,
- paint in the second color the elements: $a_2=6$ , $a_5=3$ and $a_8=3$ ,
- paint in the third color the element $a_3=5$ ,
- paint in the fourth color the element $a_1=7$ .